THE  MAGNETIZATION  OF  COBALT  AS  A 
FUNCTION  OF  THE  TEMPERATURE 
AND  THE  DETERMINATION  OF  ITS 
INTRINSIC  MAGNETIC  FIELD 


by 

WILLIAM  WARREN  STIFLER 

A.  B.  Shurlleff  College,  1902 
A.  M.  University  of  Illinois,  1008 


THESIS 

Submitted  in  Partial  Fulfillment  of  the  Requirements 
for  the  Degree  of  Doctor  of  Philosophy  in 
Physics  in  the  Graduate  School  of 
the  ltniversity  of  illinois 
1911 


Press  of 
The  New  Era  Printing  Co. 
Lancaster,  Pa. 
1911 


(Reprinted  from  the  Physical  Review,  Vol.  XXXIII.,  No.  4.  October,  ion.) 


THE  MAGNETIZATION  OF  COBALT  AS  A  FUNCTION  OF 
THE  TEMPERATURE  AND  THE  DETERMINATION 
OF  ITS  INTRINSIC  MAGNETIC  FIELD. 

By  W.  W.  Stifler. 

Introduction. 

THOUGH  cobalt  has  always  been  classed  as  one  of  the  strongly 
magnetic  metals,  its  properties  do  not  seem  to  have  been  studied 
with  the  interest  manifested  in  those  of  iron  and  nickel.  In  spite  of 
the  work  of  E.  Becquerel,1  Pliicker,2  Rowland,3  Hankel,4  H.  Becquerel,5 
Gaiffe,6  Trowbridge  and  McRea,7  Berson,8  Bidwell,9  Ewing  and  Low,10 
duBois,11  Fleming,  Ashton  and  Tomlinson,12  Beattie,13,  and  Nagaoka  and 
Honda,14  until  very  recently  the  amount  of  real  numerical  data  on  the 
magnetic  properties  of  cobalt,  even  at  ordinary  temperatures,  was  very 
meagre. 

Within  the  last  two  years  several  articles  have  been  published  which 
are  of  great  interest  from  a  theoretical  point  of  view.  One  of  these  is 
by  P.  Weiss15  and  gives  the  results  of  work  at  ordinary  temperatures; 
another  is  by  Weiss  and  Kamerlingh  Onnes16  and  gives  the  results  of  their 
work  at  very  low  temperatures.  In  the  investigation  described  in  the 
first  of  these  papers,  the  saturation  value  of  the  specific  intensity  of 

1  Comp.  Rend.,  20,  pp.  1708-1711,  1845. 
'Pogg.  Ann.,  91,  pp.  1-56,  1854. 
sPhil.  Mag.,  164,  pp.  321-340,  1874. 
•Ann.  der  Physik,  N.  F.  1,  pp.  285-296,  1877. 

'Ann.  de  Chim.  et  de  Phys.,  Ser.  5,  16,  pp.  227-286,  1879;  Comp.  Rend.,  88,  pp.  111-114 
1879- 

'Comp.  Rend.,  93,  pp.  461-462,  1881. 

7  Proc.  Am.  Acad.  Arts  and  Sciences,  20,  pp.  462-472,  1884-85. 

'Journal  de  Physique,  is,  pp.  437-456,  1886;  Ann.  de  Chim.  et  de  Phys.,  Ser.  6,  8,  pp. 
433-502,  1886;  Lum.  Electr.,  21,  pp.  259-267,  1886. 

'Phil.  Trans.  Roy.  Soc.  London,  179A,  pp.  205-230,  1888.    For  cobalt  see  p.  215. 

10  Phil.  Trans.  Roy.  Soc.  London,  180A,  pp.  221-244,  1898. 

"Phil.  Mag.,  195,  pp.  293-306  and  pp.  253-267,  1890. 

12  Phil.  Mag.,  214,  pp.  271-279,  1899. 

"Phil.  Mag.,  217,  pp.  642-647,  1901. 

14  Phil.  Mag.,  220,  pp.  45-72,  1902. 

"Journal  de  Physique,  Ser.  4,  9,  pp.  373-393,  1910;  Archives  des  Sciences  (Geneve), 
Ser.  4,  29,  pp.  175-203,  1910. 

"Journal  de  Physique,  Ser.  4,  9,  pp.  555-584,  1910;  Konink.  Akad.  Wetensch.  Amsterdam, 
Proc.  12,  pp.  649-677,  1910;  Comp.  Rend.,  150,  pp.  686-689,  1910. 


269 


W.  IF.  STIFLER. 


[Vol.  XXXIII. 


magnetization — that  is,  the  intensity  of  magnetization  per  gram — was 
determined.  Weiss  found  that  the  law  of  approach  to  saturation  at 
1 7°  C.  for  cobalt  was  given  by  the  equation 


where  a  is  the  specific  intensity  of  magnetization.  By  plotting  u  as  a 
function  of  I /IP  and  extrapolating  he  found  the  saturation  value  to  be 
162  at  1 70  C.  These  results  were  confirmed  by  the  work  of  Droz1  pub- 
lished at  the  same  time.  In  the  second  investigation  measurements  were 
taken  at  temperatures  as  low  as  that  of  liquid  hydrogen.  The  value  of 
<r  at  these  very  low  temperatures  was  found  to  be  less  than  163.6. 

Very  recently  Weiss2  has  measured  the  specific  susceptibility  of  cobalt 
in  the  temperature  interval  from  11560  C.  to  13020  C.  using  a  method 
similar  to  that  employed  by  Curie  in  his  classical  researches  on  the 
magnetic  properties  of  bodies  at  high  temperatures.3  This  article  was 
published  some  months  after  the  present  investigation  was  undertaken. 
Weiss  states  that  the  "Curie  point"  for  cobalt  is  probably  in  the  neigh- 
borhood of  mo°  C. 

The  recent  developments  of  the  electron  theory  of  magnetism  make 
a  knowledge  of  the  saturation  value  of  the  intensity  of  magnetization  as 
a  function  of  the  temperature  of  great  theoretical  interest  and  the  present 
investigation  was  undertaken  with  the  objects: 

1.  To  determine  the  specific  intensity  of  magnetization  at  various 
temperatures  up  to  about  11500  C;  that  is,  to  a  temperature  somewhat 
above  that  at  which  spontaneous  fcrro-magnetism  disappears. 

2.  To  deduce  from  these  data  the  value  of  the  intrinsic  molecular 
field  of  cobalt  and  the  moment  of  its  elementary  magnet. 


For  this  purpose,  the  method  used  by  Weiss4  seemed  best  adapted.  It 
consists  essentially  in  observing  the  throw  of  a  ballistic  galvanometer  con- 
nected in  series  with  a  helix  placed  in  a  strong  longitudinal  magnetic  field 
w  ben  an  ellipsoid  of  the  substance  to  be  tested  is  suddenly  jerked  out  of  the 
helix.  The  throw  of  the  galvanometer  is  then  compared  with  that  pro- 
duced when  a  known  current  is  made  or  broken  through  the  primary  of  a 
st.md.ird  helix,  the  secondary  of  which  is  included  in  the  galvanom- 

1  Archives  det  Sciences  (Geneve),  Ser.  4.  20.  pp.  204-224  and  290-309,  1910. 

•Archives  des  Sciences  (Geneve),  Ser.  4,  31.  pp.  5-19  and  89-117,  191 1. 

•Ann.  dr  (  him.  et  dr  I'hys.,  Ser.  7.  ?,  pp.  2K9  »".S,  iR9SI  Oiuvrcs,  pp.  232-334. 

4  I  •:•  I'll'.  1  1  1.  .  s.-i    |.  ij,  |>p   (7i  y>\.  kjio;  Archive*  dot  Science*  (Geneve),  Ser. 

4.  jv.  pp.  « 75-203.  1910. 


10 

a  =  162  (1  -  I. II  — ), 


MKTIIOI). 


No.  4-1 


MAGNETIZATION  OF  COBALT. 


27O 


^ — 


eter  circuit.  The  connections  are  shown  diagrammatically  in  Fig.  1, 
where  C  is  the  cobalt  ellipsoid;  H  is  the  induction  helix  connected 

in  series  with  the  controlling  resistance,  R', 
the  galvanometer,  G,  and  the  secondary,  S,  of 
the  standard  helix;  P  is  the  primary  of  the 
standard  helix;  R,  the  controlling  resistance; 
and  A  is  a  carefully  calibrated  ammeter. 

The  formulae  for  a  and  I  by  this  method  are 
easily  shown  to  be 


mn'Aji  -  dtW)  V  d  =  R  d 
iow«(i  —  di\2li)  d' 


and 


Fig.  1. 


_  nm'A  (I  -  d1W)  r 
1  ~  ioVn(i  -  df/2h2)  'd' 


where  A 

area  of  cross  section  of  primary  of  standard  helix. 

number  of  turns  per  cm.  on  primary. 

N' 

total  number  of  turns  on  secondary. 

h 

length  of  primary. 

diameter  of  primary. 

n 

number  of  turns  per  centimeter  on  H. 

k 

length  of  H. 

di 

diameter  of  H. 

m 

mass  of  C. 

V 

volume  of  C. 

d 

deflection  of  galvanometer  when  C  is  jerked  out  of  H. 

d' 

deflection  when  current  is  made  or  broken  through  primary.. 

V 

current  in  amperes  through  primary. 

The  advantage  of  using  a  rather  than  I  lies  in  the  fact  that  <r  is  inde- 
pendent of  changes  in  density  or  volume  due  to  changes  in  temperature. 
The  value  of  the  field  H  inside  the  ellipsoid  for  an  external  field  of  H0  is1 

H  =  Ho  -  LI, 

where  L  is  the  demagnetizing  factor  of  fne  ellipsoid. 

Experimental  Details. 
Magnet. — The  magnetic  field  was  obtained  by  means  of  a  large  electro- 
magnet of  the  duBois  type.    The  core  was  approximately  10  cm.  in 
diameter.    For  this  work  it  was  equipped  with  a  pair  of  conical  pole 
pieces  2.5  cm.  in  diameter  at  the  smaller  end.    A  hole  2.1  cm.  in  diameter 

1  Maxwell,  Treatise  on  Electricity  and  Magnetism,  3d  Ed.,  Vol.  II.,  §437-438,  pp.  66-69. 


271 


W.  W.  STIFLER. 


[Vol.  XXXIII. 


was  drilled  through  these  to  permit  the  ellipsoid  to  be  withdrawn.  The 
magnet  would  carry  25  amperes  for  several  minutes  without  undue 
heating.  For  each  air-gap  used,  the  strength  of  the  field  at  the  center 
was  determined  by  means  of  a  flip  coil  and  ballistic  galvanometer  cali- 
brated by  comparison  with  a  standard  helix.  The  field  was  also  measured 
with  a  magnetic  balance  made  by  Weber  in  Zurich  and  practically 
identical  with  the  one  described  by  Weiss.1  The  results  obtained  by 
the  two  methods  were  in  close  agreement.  For  convenience,  the  value 
of  the  field  for  currents  from  2  to  25  amperes  was  determined  by  steps 
of  two  or  three  amperes.  From  these  data  curves  were  plotted  giving 
H  as  a  function  of  the  current,  the  scale  being  such  that  I  cm.  was 
equivalent  to  100  or  200  lines  per  square  centimeter. 

Galvanometer. — The  galvanometer  used  was  a  Leeds  and  Northrup 
type  H  instrument.  It  had  a  resistance  of  26.4  ohms,  a  ballistic  sensi- 
bility of  45.6  mm.  per  microcoulomb  on  open  circuit  with  a  scale  distance 
of  50  cm.,  and  a  period  of  12.7  seconds  on  open  circuit.  The  scale  used 
had  500  divisions  in  a  length  of  25  cm.  and  was  made  by  photography 
from  a  very  accurate  50  cm.  scale.  The  sensitiveness  was  further  in- 
creased by  placing  the  scale  at  a  distance  of  approximately  three  meters. 
With  this  arrangement  the  "throw"  could  be  read  accurately  to  0.5  of 
a  scale  division  or  even  less  As  the  instrument  as  used  was  on  closed 
circuit,  it  was  practically  aperiodic,  and  its  sensitiveness  was  considerably 
reduced. 

Heating  Apparatus. — The  induction  helix  was  used  as  the  core  around 
which  was  built  up  a  small  electric  furnace  to  give  the  necessary  tem- 
peratures. For  various  reasons  two  separate  pieces  of  apparatus  were 
built,  one  for  the  lower  temperatures,  the  other  for  the  higher  tempera- 
tures. 

Up  to  5500  C.  the  apparatus  shown  in  section  in  Fig.  2  was  used. 
The  induction  helix  was  of  No.  30  bare  copper  wire  wound  on  a  hard 
glass  tube.  The  wire  was  held  in  place  bycacmentium  and,  where  neces- 
sarv,  libers  of  asbestos  were  worked  in  between  the  individual  turns. 
There  were  89  turns  in  a  length  of  4  cm. 

The  heating  coils  were  of  No.  16  german  silver  wire  and  were  insulated 
from  the  induction  helix  by  a  glass  tube  as  shown.  In  order  to  decrease 
the  temperature  ^radi<  nl  .it  the  center  of  the  induction  helix,  two  heating 
( <>ilv  were  us<  d.  'I  lu-  inner  one  was  wound  as  regularly  as  possible,  while 
ilu  outer  one  was  wound  closely  at  the  ends  but  with  the  turns  much 
farther  apart  at  the  middle.    The  two  coils  were  separated  from  each 

'Journal  tie  I'hyniquc.  .16.  pp.  43»"435.  I9°7-    Sec  nl»o  L'licluiraKc  Klcclriquc.  24,  pp. 

357  266,  1900,  ami  Journal  da  i'iiy»iquc.  20.  pp-  383-390.  1900. 


No.  4-] 


MAGNETIZATION  OF  COBALT. 


272 


other  by  mica.  In  order  to  reduce  the  magnetic  effect  of  the  heating 
currents,  the  two  coils  were  always  connected  so  that  they  opposed  each 
other  magnetically.  By  properly  adjusting  the  currents  in  the  two  coils, 
the  temperature  at  the  center  of  the  helix  could  be  made  constant  to 
within  2°  C.  over  a  distance  of  10  to  15  mm.  The  coils  were  packed  in 
loose  asbestos,  and  the  whole  apparatus  was  covered  with  asbestos  board. 

Owing  to  the  fact  that  at  the  higher  temperatures  saturation  is  reached 
at  lower  fields,  the  apparatus  used  for  temperatures  above  5500  C.  was 


I  3i      <i      Si      4.,      t,      a,      9,  id 

Cm. 

Fig.  2. 

5,  induction  helix;  Hi,  primary  heating  coil;  Hi,  secondary  heating  coil;  NS,  magnet; 
C.  cobalt  ellipsoid;  AB,  asbestos  board;  AF,  asbestos  fiber;  GG,  glass  tubes;  M,  mica; 
XX,  galvanometer  circuit. 

somewhat  larger  though  of  similar  design.  The  core  of  the  induction 
helix  was  a  clear  quartz  tube.  The  helix  was  of  No.  30  bare  platinum 
wire  wound  in  two  layers  separated  from  each  other  by  mica.  The 
individual  turns  were  separated  from  each  other  by  asbestos  yarn. 
Though  the  insulating  power  of  this  broke  down  considerably  above 
iooo0  C,  actual  tests  showed  that  this  did  not  introduce  any  appreciable 
error. 

The  heating  coils  were  of  No.  13  nickel  wire  and  were  separated  from 
the  helix  by  a  tube  of  fused  silica.  Since  nickel  loses  its  magnetic  prop- 
erties at  3600  C,  no  error  was  introduced  by  its  use.  The  primary 
heating  coil  was  wound  in  two  layers.  Asbestos  yarn  was  used  to 
separate  the  individual  turns,  while  the  layers  were  insulated  from  each 
other  by  mica.  The  secondary  heating  coil  consisted  of  one  layer  and 
was  wound  as  in  the  other  apparatus. 


273 


W.  W.  STIFLER. 


(Vol.  XXXIII. 


Calcined  magnesia  contained  in  a  porcelain  ring  was  used  as  an  heat 
insulator  next  to  the  coils.  Outside  of  this  a  layer  of  magnesia  packing 
such  as  is  used  for  high  pressure  steam  pipes  was  used.  The  whole 
apparatus  was  covered  with  asbestos  board.  It  is  shown  in  section  in 
Fig.  3.  The  heating  coils  on  this  apparatus  burned  out  several  times 
during  the  course  of  the  experiments  but  they  were  rewound  and  the 
apparatus  rebuilt  in  substantially  the  same  way  each  time.  The  induc- 
tion helix  was  not  injured  in  any  way. 


~  •    '<    »         »    »■  »i 

cm 

Fig.  3. 

Si.  induction  helix;  St.  fused  silica  tube;  Hi,  primary  heating  coil;  Hi.  secondary  heating 
coil;  M.  mica  insulation;  A.  asbestos  board;  P,  porcelain  ring;  (),  quartz  tube;  X,  galva- 
nometer circuit. 

Temperature  Measurements. — Temperatures  were  measured  with  a 
thermocouple.  A  Wolff  potentiometer  and  Weston  standard  cell  were 
used  to  measure  itsc.m.f.,  and  the  resistance  in  the  galvanometer  circuit 
was  adjusted  so  that  the  instrument  read  directly  to  one  microvolt. 
The  method  of  reading  and  calibration  was  essentially  that  described  by 
Clement  and  Fgy.1  For  temperatures  between  ioo°  C.  and  4200  C,  a 
copper-platinum  thermocouple  was  used.  As  this  has  an  inversion  point 
.it  .,l.oin  Oo  C,  it  was  not  um  (|  below  100"  ( '.  It  was  calibrated  by  the 
boiling  point  of  water,  the  freezing  point  of  zinc,  and  by  several  inter- 

'  Univ.  01  III.  Eng.  Iixp.  Station  Bulletin  No.  36,  1909. 


No.  4.] 


MAGNETIZATION  OF  COBALT. 


274 


mediate  points  lying  between  1200  C.  and  2500  C.  which  were  determined 
by  comparison  with  a  carefully  calibrated  mercury  thermometer.  The 
temperatures  were  read  from  the  corresponding  e.m.f.'s  by  a  calibration 
curve  plotted  to  such  a  scale  that  1  mm.  corresponded  to  i°  C. 

For  temperatures  above  4200  C,  a  platinum  platinum-rhodium  couple 
was  used.  This  was  calibrated  at  the  freezing  points  of  zinc,  silver,  and 
copper.  From  these  three  points  the  three  constants  of  the  standard 
parabolic  equation  were  calculated.  The  couple  as  used  was  easily  sensi- 
tive to  1  microvolt — equivalent  to  about  o.i°  C. — at  11000  C.  The 
temperatures  as  read  from  either  couple  are  probably  accurate  at  i°  C. 

P reparation  and  Mounting  of  the  Ellipsoids. — The  first  samples  of  cobalt 
obtained  were  in  the  form  of  small  lumps  3  or  4  mm.  in  diameter.  Several 
attempts  were  made  to  fuse  these  into  a  button,  using  first  a  small  assay 
furnace  and  later  a  coke  furnace.  These  attempts  proved  futile,  owing 
to  the  very  high  melting  point  of  cobalt — 1489. 8°  C. 

After  one  or  two  preliminary  trials,  a  button  weighing  about  200  grams 
was  prepared  from  the  oxide  by  the  Goldschmidt  process.  From  this 
two  rings  were  turned  and  tested  by  the  ring  method.  The  tests  on 
the  larger  ring — No.  1 — gave  values  of  B  of  only  about  one  tenth  the 
magnitude  to  be  expected.  Annealing  for  several  hours  at  white  heat 
improved  this  decidedly,  though  the  results  were  still  only  about  one 
third  of  the  accepted  values.  The  smaller  ring — No.  2 — gave  similar 
results  without  being  annealed.  Analysis  showed  that  these  samples 
contained  about  1  per  cent,  of  aluminum. 

One  hundred  grams  of  cobalt  in  rectangular  sheets  about  6  cm.  X  10 
cm.  X  0.05  cm.  were  then  obtained  from  Kahlbaum  through  Eimer  and 
Amend.  Tests  on  a  ring — No.  3 — made  by  building  up  five  layers  of  this 
showed  that  its  magnetic  properties  were  excellent  (see  Fig.  4). 

To  get  this  material  into  a  form  from  which  ellipsoids  could  be  ground, 
it  was  necessary  to  fuse  it  into  a  button  or  rod.  At  first  this  was  accom- 
plished by  means  of  a  vertical  platinum  resistance  furnace,  using  a 
maximum  power  consumption  of  approximately  2,200  watts.  A  No.  o 
black  lead  crucible,  lined  with  a  paste  of  98  per  cent,  magnesite  and  2 
per  cent,  bone  ash,  was  used.  After  the  lining  was  thoroughly  dry,  a 
charge  of  about  20  grams  of  metal  was  put  in  and  this  was  covered  with 
a  layer  of  borax  glass.  After  several  hours  the  cobalt  fused,  giving  a 
very  homogeneous  button  about  2  cm.  in  diameter  and  0.6  cm.  thick. 

An  attempt  to  repeat  the  process  resulted  in  burning  out  the  furnace 
before  the  cobalt  was  entirely  fused.  However  one  piece  was  obtained 
from  which  it  was  possible  to  turn  an  ellipsoid. 

After  considerable  practice  it  was  found  possible  to  prepare  the  material 


275 


n*.  ir.  STIFLER. 


[Vol.  XXXIII. 


by  melting  it  in  a  fused  silica  tube  held  in  an  arc.  Owing  to  the  impos- 
sibility of  securing  anything  like  uniform  heating  over  even  a  short 
distance,  it  was  only  with  great  difficulty  that  two  or  three  rods  ap- 
proximately 0.5  cm.  in  diameter  and  1.0  cm.  to  1.2  cm.  long  were  obtained 
by  this  method. 

The  ellipsoids  were  ground  from  the  rods  on  a  Landis  Universal 
Grinder,  using  an  alundum  wheel  with  a  properly  shaped  rim.  After 
grinding,  the  accuracy  of  the  shape  was  tested  and  found  to  be  satis- 
factory by  projecting  the  enlarged  shadow  of  the  ellipsoids  with  an 
Edinger  Drawing  Apparatus. 


10 

000 

I 

000  ^ 

,0  / 

«  1 

/  4 

000  /  / 

rff     /  f, 

0  a 

.  . 

If  *» 

/  2 

006  / 

R.'nf  Us  : 

/o 

O06 

Kig.  4. 


In  all,  five  ellipsoids  of  revolution,  approximately  1  cm.  long  and  0.45 
cm.  in  diameter,  were  prepared.  Complete  sets  of  data,  however,  were 
carried  out  for  only  two.  The  ellipsoids  were  distinguished  for  con- 
venience as  A,  B,  C,  D,  and  E.  The  method  of  preparing  each  is  given 
below,  and  a  summary  of  their  dimensions  is  given  in  Table  I. 

A — made  from  first  melting  in  resistance  furnace.  C  ross-section  very 
accurate. 

B—  made  from  the  same  button  as  A.  Not  quite  as  perfect  cross- 
section  as  A. 

C—  made  from  rod  prepared  by  melting  the  metal  in  fused  silica  tube 
h<  Id  in  arc.    Cross-section  fairly  accurate. 

D — made  from  sample  melted  in  silica  tube  in  arc.  Cross-section 

fairly  accurate. 


No.  4.] 


MAGNETIZATION  OF  COBALT. 


276 


E — made  from  second  melting  in  resistance  furnace.  Cross-section 
fairly  accurate  except  for  very  slight  pit  near  one  end. 


Table  I. 


Mean 
Diam. 

Spec. 
Grav. 

Volume  by 

Length. 

Mass. 

Displac.  of 
Water. 

Calcula- 
tion. 

e 

A 

0.9965 

0.4475 

0.8633 

8.25 

0.1047 

0.1045 

0.8934 

1.9385 

B 

0.9330 

0.4480 

0.8412 

8.24 

0.1021 

0.0981 

0.8770 

2.0890 

C 

0.9370 

0.4110 

0.6804 

8.80 

0.0773 

0.0829 

0.8986 

1.8888 

D 

0.9960 

0.4430 

0.8275 

8.74 

0.0947 

0.1023 

0.8956 

1.9177 

E 

0.9920 

0.4250 

0.8528 

8.73 

0.0977 

0.0938 

0.8992 

1.8817 

In  some  of  the  later  work,  C  and  E  became  more  or  less  oxidized. 
In  each  case  the  oxide  was  carefully  removed  with  fine  emery  cloth  and 
the  specimen  was  carefully  polished  with  crocus  cloth  and  weighed. 
Measurements  showed  that  the  shape  of  the  ellipsoids  was  not  altered 
appreciably  by  this  process. 

The  reason  for  the  low  specific  gravity  of  A  and  B  is  unexplained  as  yet. 

A  chemical  analysis  of  the  original  material  showed  that  it  was  100 
per  cent,  pure,  with  the  possibility  of  a  trace  of  nickel. 

For  temperatures  below  4200  C,  the  ellipsoids  were  mounted  in  glass 
tubes  sealed  at  one  end.  The  thermocouple  was  inserted  through  the 
other  end  and  the  junction  was  separated  from  the  cobalt  by  a  thin  layer 
of  mica.    As  a  rule  the  junction  was  about  one  third  of  the  total  length 

(GlaSS)  ~T/(S..l.n,W«x) 


(Quart*)  — ^p^eiSSo  '~W 

Fig.  5. 

of  the  ellipsoid  from  the  end.  For  temperatures  above  3000  C.  the  end 
of  the  tube  through  which  the  thermocouple  was  inserted  was  sealed 
with  sealing  wax,  and  the  whole  tube  was  exhausted  and  sealed  to  avoid 
oxidation  of  the  ellipsoid. 

For  temperatures  above  420°  C.  a  clear  quartz  tube  was  used  to  hold 
the  ellipsoid.    A  glass  tube  was  joined  to  the  open  end  of  this  for  con- 


277 


W.  IT'.  STIFLER. 


[Vol.  XXXIII. 


venience  in  exhausting.  No  particular  difficulty  was  experienced  in 
making  the  joints  air  tight  with  sealing  wax,  but  at  the  higher  tempera- 
tures the  quartz  devitrified  upon  prolonged  heating  and  the  end  became 
"chalky."  In  this  condition  it  would  admit  air  and  in  one  or  two  in- 
stances as  noted  above  the  specimens  were  oxidized  in  attempting  to 
carry  out  a  second  set  of  readings.  Eventually  it  was  found  necessary 
to  re-seal  the  end  of  the  tube  and  exhaust  the  tube  anew  after  each  set 
of  readings.    Fig.  5  shows  the  two  methods  of  mounting. 

Procedure  in  Taking  Readings. 

The  general  method  of  taking  readings  was  as  follows.  The  furnace 
was  heated  for  several  hours  until  thermal  equilibrium  was  established. 
It  was  found  necessary  to  draw  the  heating  currents  from  a  large  storage 
battery  as  the  variation  of  0.1  ampere  caused  a  very  appreciable  change 
in  temperature.  For  the  higher  temperatures  heating  currents  of  15  to 
20  amperes  were  used.  When  everything  had  reached  a  steady  state, 
the  tube  containing  the  ellipsoid  and  thermocouple  was  inserted.  The 
position  of  the  tube  to  bring  the  ellipsoid  into  the  center  of  the  helix 
was  approximately  determined  by  throwing  on  the  magnetic  field  for  a 
moment.  The  tube  was  then  moved  by  steps  of  2  to  5  mm.  along  the 
helix,  and  readings  of  the  temperature  at  each  position  were  taken  after 
sufficient  time  had  elapsed  for  the  cobalt  to  take  up  the  temperature  of 
its  surroundings.  As  there  is  usually  comparatively  little  lag  in  the 
readings  of  a  thermocouple,  the  fact  that  sometimes  as  many  as  twelve 
or  fifteen  minutes  were  required  before  its  readings  became  constant 
indicated  that  the  thermocouple  was  registering  the  actual  temperature 
of  the  cobalt.  Usually  it  was  possible  to  adjust  the  heating  currents 
so  that  a  change  of  a  centimeter  in  the  position  of  the  cobalt  produced 
a  change  of  only  2°  or  in  the  readings  of  the  thermocouple.  At  the 
lower  temperatures  it  was  possible  to  do  much  better  than  this.  Under 
tiller  circumstances,  the  assumption  that  the  temperature  of  the  ellipsoid 
was  uniform  to  at  least  l°  C.  seemed  justifiable. 

The  ellipsoid  was  placed  in  the  position  indicated  as  that  at  the  highest 
temperature,  and  the  tube  was  marked  so  that  it  was  possible  to  replace 
it  exactly  in  this  position.  When  the  ellipsoid  had  reached  thermal 
equilibrium,  the  reading  of  the  thermocouple  was  taken,  the  magnetic 
luld  was  thrown  on,  and  the  dellection  of  the  galvanometer  when  the 
ellipsoid  was  jerked  out  of  I  he  helix  was  noted.  The  magnetic  field  wa« 
then  thrown  off  and  the  ellipsoid  was  replaced  in  position  and  allowed 
t<>  o  .1111  its  former  temperature.  As  a  rule,  three  readings  were  taken 
al  •  ,i<  h  held  strength  and  the  mean  of  the  deflections  w.ls  used  in  calculate 


No.  4.] 


MAGNETIZATION  OF  COBALT. 


278 


ing  /  and  a.  At  the  lower  temperatures  these  readings  usually  agreed  to 
half  a  scale  division  in  two  hundred  or  more.  At  the  higher  temperatures 
they  were  not  so  great  and  the  agreement  was  not  quite  so  good.  However 
the  readings  as  a  whole  were  very  consistent  even  under  these  circum- 
stances, usually  agreeing  with  each  other  to  within  I  per  cent,  or  at  most 
2  per  cent,  up  to  9000  C.  The  reading  of  the  thermocouple  was  taken 
each  time  just  before  the  ellipsoid  was  withdrawn,  and — as  a  rule — these 
readings  were  not  allowed  to  differ  by  more  than  15  microvolts,  corre- 
sponding to  1. 50  C,  during  a  set  of  readings.  At  the  very  high  tempera- 
tures where  the  cobalt  was  especially  sensitive  to  changes  of  temperature, 
the  variation  was  made  even  less.  The  mean  of  the  thermo-couple  read- 
ings was  used  in  calculating  the  temperature. 

After  nearly  every  set  of  readings,  the  galvanometer  was  calibrated 
by  means  of  the  standard  helix.  The  current,  I',  for  this  purpose  was 
read  by  a  Siemens  and  Halske  milliammeter  which  had  been  calibrated 
with  a  standard  ohm  coil  and  potentiometer.  For  temperatures  up  to 
10000  C,  the  values  of  I' Id'  remained  practically  constant  and  the  mean 
value  was  used  in  calculating  a. 

The  magnetic  fields  used  ranged  from  1,600  gausses  to  6,900  gausses 
for  the  lower  temperatures,  giving  fields  of  from  800  gausses  to  5,000 
gausses  inside  the  ellipsoids.  As  these  were  insufficient  to  produce 
saturation  below  3500  C,  the  saturation  values  were  determined  by  an 
extrapolation  similar  to  that  of  Weiss  mentioned  above.  As  neither 
a  and  i/H  nor  a  and  1/H2  gave  a  straight  line,  both  were  plotted  and  the 
mean  of  the  values  was  used.  The  results  at  these  lower  temperatures 
were  not  used  in  the  theoretical  deductions  so  that  extreme  accuracy  in 
the  extrapolated  results  is  not  important.  Above  3500  C.  saturation 
could  be  reached  with  the  fields  used,  and  at  the  higher  temperatures 
fields  as  low  as  3,500  gausses  produced  saturation.  The  values  of  the 
magnetic  field  were  corrected  for  the  magnetic  effect  of  the  heating 
coils  whenever  this  effect  was  appreciable. 

In  the  interval  between  10500  C.  and  11000  C.  it  was  very  difficult 
to  obtain  consistent  readings,  as  a  very  slight  change  in  temperature 
produced  a  marked  change  in  a.  At  these  higher  temperatures  also 
thermoelectromotive  effects  in  the  galvanometer  caused  some  difficulty, 
rendering  the  zero  of  the  galvanometer  somewhat  uncertain  at  times  and 
often  causing  it  to  drift  steadily  in  one  direction.  These  difficulties 
were  remedied  in  large  measure  by  keeping  the  junctions  of  the  platinum 
leads  from  the  helix  and  the  copper  connecting  wires  at  o°  C. 


H".  TV.  STIFLER. 


[Vol.  XXXIII. 


Data. 

The  data  obtained  for  ellipsoids  C  and  E  are  summarized  in  the  fol- 
lowing tables.  Tables  II.  and  III.  give  the  values  of  H  and  <r  as  observed 
at  various  temperatures,  and  the  values  of  exK.  Table  IV.  gives  a  sum- 
mary of  this.  Fig.  6  shows  the  method  of  determining  <rx  below  4000  C. 
by  extrapolation.  The  extrapolated  values  are  probably  accurate  to  1 
per  cent.  Curve  A  in  Fig.  7  shows  <x  as  a  function  of  the  temperature. 
The  close  agreement  between  the  results  for  ellipsoids  C  and  E  argues 
for  the  accuracy  of  the  data. 

From  the  data  we  can  also  calculate  B  and  draw  magnetization  curves 
for  high  fields  at  various  temperatures.  Several  of  these  curves  are 
shown  in  Fig.  8. 

Theoretical  Considerations. 
In  his  article  upon  the  magnetic  properties  of  bodies  at  high  tempera- 
tures to  which  reference  was  made  above,  Curie  called  attention  to  the 

Table  II. 

Ellipsoid  C. 


C. 

130°  C. 

335°  C.  * 

307 

0  c. 

4M°  C. 

H 

a 

If 

a 

H 

1  " 

H 

II 

a 

725 

102.4 

713 

103.0 

625 

108.4 

500 

115.9 

460 

119.2 

1,955 

139.6 

2.154 

114.2 

1,984 

149.2 

1,980 

149.6 

2,055 

145.8 

2,985 

149.1 

3,031 

151.5 

3,026 

151.8 

3,060 

149.9 

3,135 

146.3 

3,450 

153.2 

3,774 

153.5 

3,816 

152.5 

3,825 

150.4 

3,930 

146.4 

3,955 

154.6 

4,200 

153.3 

4,386 

152.8 

4,425 

150.4 

4,515 

146.4 

4,270 

155.2 

=  161.0 

=  158.5 

=  154.0 

=  151.0 

=  146.4 

54,0  c. 

698 

°c. 

874 

°c. 

991°  C. 

K'43 

°c. 

H 

a 

H 

a 

H 

H 

a 

II 

a 

445 

120.2 

140 

87.5 

215 

83.4 

370 

72.3 

770 

46.4 

2,160 

139.9 

855 

124.1 

1,300 

97.9 

1,680 

72.1 

2,070 

47.5 

3,250 

139.6 

1,620 

124.3 

2,015 

97.9 

2,385 

73.1 

2,780 

49.1 

4,015 

140.2 

2,115 

125.2 

2,510 

98.7 

2,880 

73.3 

3,290 

48.9 

4,610 

140.0 

2,400 

124.9 

3,915 

97.9 

3,335 

71.9 

3,680 

49.5 

*• 

140.2 

-125.2 

=  9.X.7 

=73.3 

=49.5 

10650  C. 

108a0 C. 

1104 

0  C. 

°c. 

H 

» 

H 

» 

II 

9 

II 

a 

1,165 

21.4 

3,250 

6.0 

1,400 

1.3 

1,370 

? 

2.4(H) 

26.8 

2,100 

1.9 

2,380 

? 

(.(H,0 

(ii  (i 

3,050 

2.6 

3,090 

? 

3,570 

29.7 

(.  W) 

? 

4.(110 

29.4 

a , 

30.0 

-6.0 

2.6(?) 

*• 

-? 

ira|>-il.it inn  from  curve*. 


No.  4I 


MAGNETIZATION  OF  COBALT. 


Table  III. 


Ellipsoid  E. 


22°  . 

127°  c. 

2320  c. 

3000  c. 

415 

3c. 

59° 

0  C. 

H 

a 

H 

XT 

H 

a 

H 

a 

H 

H 

490 

66.6 

876 

94.3 

720 

103.9 

540 

114.6 

650 

108.9 

690 

106.8 

1,285 

104.6 

2,190 

138.6 

2,050 

147.0 

2,175 

145.6 

2,160 

142.2 

2,305 

132.7 

2,575 

134.2 

3,135 

147.1 

3,115 

148.3 

3,140 

146.8 

3,240 

141.6 

3,385 

133.0 

3,260 

142.6 

3,905 

148.9 

3,930 

149.6 

3,970 

146.8 

3,990 

142.6 

4,155 

133.4 

4,065 

148.3 

4,225 

149.5 

4,930 

149.0 

4,505 

147.3 

4,625 

141.2 

4,760 

132.9 

4,445 

149.6 

axx  - 

161.0 

ir^i  = 

154.0 

«V  = 

150.5 

148.0 

<r  =  142.3 

"ao  = 

133.1 

687°  C. 

867°C. 

I02g 

°c. 

1057°  c. 

11130  c. 

11440  c. 

165 

81.2 

200 

78.7 

710 

53.0 

850 

34.7 

3,800 

3.5 

1,420 

? 

830 

121.4 

1,210 

97.3 

1,850 

57.8 

2,750 

38.4 

2,440 

? 

1,515 

121.9 

1,950 

96.3 

1,590 

56.8 

3,185 

38.4 

3,360 

? 

2,055 

122.0 

2,450 

96.3 

3,160 

53.1 

2,450 

122.5 

2,850 

97.5 

3,570 

53.5 

"=0  = 

122.5 

°"oO  = 

97.5 

°"»  = 

57.0 

38.4 

<r=3.5 

a 

=  ? 

Table  IV. 

Saturation  value  of  &  as  a  function  of  the  temperature. 


Ellipsoid  C. 

Ellipsoid  E. 

Ellipsoid  C. 

Ellipsoid  /  . 

Temp. 

0*8) 

Temp. 

Temp. 

Temp. 

22° 

161.0 

22° 

161.0 

874° 

98.7 

867° 

97.5 

120° 

158.5 

127° 

154.0 

991° 

73.3 

1,029° 

57.0 

235° 

154.0 

232° 

150.5 

1,043° 

49.5 

1,057° 

38.4 

307° 

151.0 

300° 

148.0 

1,065° 

30.0 

1,113° 

3.5 

414° 

146.4 

415° 

142.3 

1,082° 

6.0 

1,144° 

? 

542° 

140.2 

590° 

133.1 

1,104° 

2.2 

698° 

125.2 

687° 

122.5 

1,152° 

? 

similarity  between  the  curves  showing  /  as  a  function  of  the  temperature 
for  iron  and  nickel  on  the  one  hand,  and  the  curves  showing  the  relation 
between  the  density  of  a  vapor  and  the  temperature  on  the  other  hand. 
Langevin2  a  little  later  worked  out  on  the  electron  theory  a  mathematical 
theory  of  paramagnetism  based  upon  the  assumption  that  the  molecules 
of  a  paramagnetic  substance  obey  the  gas  law.  Weiss3  extended  this 
theory  to  explain  the  phenomena  of  ferromagnetism  by  the  aid  of  the 
analogy  pointed  out  by  Curie.  The  sudden  increase  of  density  when  a 
vapor  liquefies  is  due  to  the  fact  that  an  enormous  internal  pressure  is 

1  By  extrapolation  from  curves. 

4  Ann.  de  Chim.  et  de  Phys.,  Ser.  5,  8,  pp.  70-127,  1905. 
'Journal  de  Physique,  36,  pp.  661-690,  1907. 


2Sl 


W.  W.  STIFLER. 


[Vol.  XXXIII. 


Fig.  6. 


160 

e 

e 

o  

1 

• 

>  0 

AW 

IU 

no 

to 

if  t'  Of 

dentil 

£  HILL.  

•  tun 

•  Kiu 

-  Thl.rrf 

It!  «ua  L 
H|»  (1 

LA  1     Cur  M 

imdi  c. 

Ittrt  I 

«- 

tb — a 

1 
fc> 

•  fi£ 

UltU  *M« 

m 

f;  ">('«»!• 

I  taU 

 £ 

■  * 

f„,l  C«"» 
•  * 

• 

'  t 

•  /J 

If 

1  iK  7. 


No.  4.] 


MAGNETIZATION  OF  COBALT. 


282 


suddenly  brought  into  play  in  addition  to  the  external  pressure.  Simi- 
larly Weiss  explained  the  fact  that  the  ferromagnetic  properties  suddenly 
appear  when  the  temperature  is  lowered  below  a  certain  critical  tempera- 
ture by  assuming  that  a  strong  molecular  field  is  suddenly  made  operative. 
This  field  is  due  to  the  action  of  the  molecules  upon  each  other  and  is 
called  by  Weiss  the  "intrinsic  molecular  field."  Of  course  the  analogy 
is  not  perfect  for  if  it  were  we  should  expect  the  pressure-density  curves 
at  constant  temperature  to 
show  the  phenomenon  of 
hysteresis.  Weiss  has  calcu- 
lated the  value  of  this  intrinsic 
field  for  iron,  nickel,  and  mag- 
netite. Kunz1  has  extended 
this  work  by  calculating  the 
moments  of  the  elementary 
magnets. 

Before  outlining  the  theory 
as  developed  by  these  investi- 
gators, the  terms  diamagnetic, 
paramagnetic,  and  ferromag- 
netic as  used  in  this  article 
will  be  defined. 

Diamagnetic  substances  are 
those  in  which  the  induced 
polarity  opposes  that  of  the 
inducing  field. 

Paramagnetic  substances 
are  magnetized  feebly  in  the 
direction  of  the  magnetizing  field.  The  susceptibility  is  independent 
of  the  field  strength  and  is  inversely  proportional  to  the  absolute  tem- 
perature according  to  Curie. 

Ferromagnetic  substances  are  very  strongly  magnetized  in  the  direction 
of  the  magnetizing  field.  The  susceptibility  is  a  very  complicated  func- 
tion of  the  field  strength  and  the  temperature.  The  phenomena  of 
hysteresis  are  characteristic  of  ferromagnetic  substances. 

The  phenomena  of  diamagnetism  are  accounted  for  by  assuming  that 
each  atom  contains  at  least  one  electron  revolving  in  an  orbit  which  lies 
wholly  within  the  atom.  The  orbits  of  the  electrons  are  so  arranged  that 
their  external  moment  is  zero.  Since  temperature  affects  the  molecule 
rather  than  the  atom,  the  purely  diamagnetic  properties  should  be  in- 

1  Phys.  Rev.,  30,  pp.  359-370,  1910. 


W.  W.  STIFLER. 


[Vol.  XXXIII. 


dependent  of  the  temperature.  It  is  probable  that  even  the  paramagnetic 
and  ferromagnetic  bodies  also  contain  electronic  orbits  which  give  them 
diamagnetic  properties,  but  the  effect  is  masked  by  the  stronger  opposing 

phenomena. 

In  the  paramagnetic  and  ferromagnetic  bodies,  the  revolving  electrons 
are  so  arranged  that  there  is  no  resulting  external  moment.  Curie1  showed 
experimentally  for  a  number  of  paramagnetic  bodies  that  the  paramag- 
netic susceptibility,  k  =  I  H,  is  inversely  proportional  to  the  absolute 
temperature.  This  is  known  as  Curie's  Law.  Langevin,  in  his  article 
to  which  reference  has  already  been  made,  has  given  a  theoretical  deduc- 
tion of  this  law.  Though  some  very  recent  experimental  results2  seem 
to  contradict  Curie's  Law,  still  on  the  whole  it  agrees  with  the  experi- 
mental facts  in  a  large  number  of  cases. 

The  present  theory  as  developed  by  Langevin,  Weiss,  and  Kunz  may 
be  outlined  as  follows.  In  a  gas  at  uniform  temperature,  not  subject 
to  the  action  of  gravity,  the  density  is  uniform  throughout.  If  gravity 
is  suddenly  allowed  to  act  upon  the  gas,  a  rearrangement  of  the  molecules 
occurs;  the  lower  layers  of  the  gas  become  more  dense,  and  the  tempera- 
ture of  the  gas  rises,  due  to  the  fact  that  a  certain  amount  of  potential 
energy  has  been  converted  into  kinetic  energy — i.  e.,  into  heat.  The 
change  of  pressure  with  height  after  equilibrium  is  established  is  now 
given  by  the  familiar  exponential  law 

p  =  />oe-por,Po, 

where  po  and  po  are  the  pressure  and  density  respectively  at  the  lowest 
layer,  and  x  is  the  height.  This  law  has  been  generalized  by  Boltzmann3 
in  the  form 

P  =  Poett,'*T, 

where  W  is  the  change  in  the  potential  energy  per  unit  distance  and  T 
and  R  are  respectively  the  absolute  temperature  and  the  universal  gas 
constant. 

The  arrangement  of  the  molecules  in  a  paramagnetic  substance  when 
not  under  the  influence  of  an  external  magnetic  field  is  exactly  analogous 
to  that  of  the  gas  molecules  when  not  under  the  influence  of  gravity, 
and  the  rearrangement  caused  by  the  action  of  a  uniform  magnetic  field 
will  follow  an  exactly  similar  law.    The  number  of  molecules,  (in,  the 

1  Ann.  dc  Chlm.  ct  de  Phys..  Ser.  7,  3,  pp.  289-405.  189s;  CEuvrcs.  pp.  332-334. 
•du  Boll  and  Honda.  Koninlt.  Akad.  Wetensch..  Amsterdam,  I'roc.  S3,  pp.  596-602, 
March.  1910. 

•  Vorlctungen  flber  Ga»-Theorle,  I  Tell,  p.  136. 


No.  4.] 


MAGNETIZATION  OF  COBALT. 


284 


directions  of  whose  axes  are  included  in  an  elementary  solid  angle,  dw, 
will  therefore  be  given  by 

dn  =  Ke"'lliTdo>,  (1) 

where  K  is  a  constant.  The  potential  energy  of  an  elementary  magnet 
of  moment  M  whose  axis  makes  an  angle  3>  with  a  uniform  magnetic  field 
His 

W  =  HM  cos  <£. 

But 

do>  —  27r  •  sin  $>  •  d$. 
Substituting  this  value  and  integrating  from  o  to  tt  we  have 

n  =  sinh  a,  (2) 

a 

where 

_  HM 
a  ~  RT 

This  result  assumes  that  the  resulting  intensity  of  magnetization  is  in 
the  same  direction  as  H.  In  general  this  will  not  be  the  case.  If  $  is 
the  angle  between  H  and  /  we  have 

dl  =  M  cos  *  dn 

and 


I  =  §a  M  cos  $  dn. 


Substituting  the  value  of  dn  from  (1)  and  integrating,  and  then  sub- 
stituting the  value  of  K  from  (2)  we  have 

cosh  a 


T  %*  I   COSh   11  1  \ 

I  =  nM  I  ~r~r —  -    )  , 
\  sinh  a      a  I 


where  n  is  the  number  of  molecules  in  unit  volume.  Since  it  is  the 
thermal  agitation  of  the  molecules  which  opposes  the  action  of  H,  if 
there  were  no  thermal  agitation — i.  e.,  if  the  substance  were  at  absolute 
zero — the  intensity  of  magnetization  would  be  a  maximum  and  we  would 
have 

Im  =  nM. 

Hence 

/  cosh  a      1  \ 

I  =  Im\  —r-r   I  ,  (3) 

\  sinh  a  at 

Since 

MH 
a  ~  RT  ' 


28S 


W.  W.  STIFLER. 


[Vol.  XXXIII. 


this  eives 


For  paramagnetic  substances,  a  is  very  small — much  less  than  unity. 

cosh  a  I 

For  values  of  a'1  less  than  tt,       —  —  -  can  be  developed  into  a  con- 

smh  a  a 

vergent  series  as  follows: 

cosh  ail         2  4 

— —  =    a  —  —  a3  +  a6  •  ■  ■ 

sinh  a      a     3        90  4542 

For  values  of  a  less  than  0.7,  the  terms  of  this  series  involving  higher 
powers  of  a  than  the  first  are  negligible,  and  we  have 

a 

'V- 

_  HPnH 
~  3~RT  ' 
=  kH. 

where  k  is  constant  for  constant  temperature,  k  is  the  paramagnetic 
susceptibility  and  is  seen  to  be  inversely  proportional  to  T,  as  found 
by  Curie  experimentally. 

In  the  case  of  ferromagnetic  substances  we  have,  in  addition  to  the 
external  field,  an  internal  or  molecular  field,  IIm.  If  this  field  acted 
alone,  the  intensity  of  magnetization  would  be  proportional  to  it  and  we 
would  have 

Hm  =  NI, 


and 


Whence 


Mil 
a  -  RT  , 

MN£ 
RT  - 


(iRT 

1  "  MX  •  (4) 


where  N  is  the  factor  of  proportionality.  Equation  (4)  shows  that  .at 
any  given  temix-rature  /  is  proportional  to  a. 

For  any  temperature  below  that  at  which  the  spontaneous  ferromagnc- 
ti-in  disappears,  tin-  value  of  /  must  satisfy  both  equations  (3)  and  (4). 
I  Molt  inn  equation  (3)  we  have  the  curve  OCA  of  Fig.  9,  while  equation  (4) 
Kives  the  straight  line  OA.    Obviously  the  values  of  /  corresponding  to 


No.  4-1 


MAGNETIZATION  OF  COBALT. 


286 


the  origin  and  to  the  point  A  satisfy  (3)  and  (4)  simultaneously.  The 
value  for  the  origin  is  for  1  =  0.  Hence  the  value  of  /  which  we  wish 
is  that  for  the  point  A. 

The  line  OA  corresponds  to  some  particular  temperature  T,  and  as  T 
varies,  OA  rotates  about  the  point  o.  If  0  denotes  the  temperature  at 
which  the  spontaneous  ferromagnetism  disappears,  the  tangent  to  the 
curve  at  the  origin  corresponds  to  T  =  9. 


Fig.  9. 


From  a  knowledge  of  the  properties  of  a  body  in  the  neighborhood  of  6 
it  is  possible  to  calculate  Hm,  the  intrinsic  molecular  field,  and  M,  the 
moment  of  the  elementary  magnet.  These  calculations  have  been  made 
for  iron,  nickel  and  magnetite.  The  results  are  given  in  Table  V.,  which 
is  taken  from  Kunz's1  article. 


Table  V. 


Substance. 

/  at  200  C. 

0 

N 

NI=Hm 

MX  102° 

Fe 

1,860 

2,120 

756°  C. 

3,850 

6,560,000 

5.15 

Fe304 

430 

490 

536°  C? 

33,200 

14,300,000 

2.02 

Ni 

500 

570 

376°  C. 

12,700 

6,350,000 

3.65 

In  order  to  make  similar  deductions  for  cobalt  from  the  experimental 
data,  the  method  of  calculating  these  quantities  will  be  indicated.  In 
the  neighborhood  of  the  point  at  which  spontaneous  ferromagnetism 
disappears,  we  have  both  the  external  field,  He,  and  the  internal  molecular 

1  Phys.  Rev.,  30,  pp.  359-370,  1910. 


287  W.W.STIFLER.  [Vol.  XXXIII. 

field,  Hm,  acting.    That  is 

_  Mff  =  M(H.  +  77m) 
a      RT  RT 
_  M(H„  +  NT) 
RT 

or 

_  M(Ht  +  NI) 
aR 

While  the  body  is  ferromagnetic  we  have 


(5) 


RT       RT  * 

For  values  of  a  less  than  0.7,  the  curve  for 

7  cosh  a  I 
7m     sinh  a  a 

is  a  straight  line,  and  we  may  take 


MH  MNI 


and 


7  _  a 

Im  m  3 


7  =  ;  7m.  (7) 


This  condition  will  certainly  hold  for  T  =  0.  Hence,  putting  7"  =  9  in 
(6)  we  have 

MNI 
Re  ' 


a  = 


Hence 


Dividing  (5)  by  (8)  we  have 

T  =  3/7.      3  7 
6  aNIm^alm' 
3H. 

or 

r  -  e  ^ 
e  "at 


_  M iV/ma 


No.  4-1 


MAGNETIZATION  OF  COBALT. 


288 


by  (7).  Hence 

(r  -  e) J  =  §  e.  (9) 

Equation  (9)  represents  an  hyperbola.  The  curves  giving  /  as  a  function 
of  T  for  iron  show  this  between  7560  C.  and  9200  C. 

To  calculate  Hm,  the  value  of  N  is  necessary.  This  may  be  determined 
from  (9)  by  taking  corresponding  values  of  I  and  H,  at  some  temperature 
above  9.    Solving  (9)  for  N  we  have 

N  9 


I  T-Q' 

I  9 
k  T  -  9  " 


(10) 


N  may  also  be  calculated  from  a  knowledge  of  Curie's  constant,  C.  By 
Curie 's  Law  we  have 

k 

C  =  XT  =  ^T, 

where  x  is  the  specific  susceptibility,  and  d  is  the  density.  But 

»-£-  1 


H     He  +  NI' 

At  T  =  9,  He  is  negligible  in  comparison  with  N.  Hence  for  this  tem- 
perature 

K  N' 


or 


or 


C~  N-dQ' 


d-C 


N  =  —.  (11) 

Having  iV  we  can  calculate  Hm,  taking  /  =  Im,  giving 

Hm  =  NIm. 

From  (8)  we  may  obtain  M,  the  moment  of  the  elementary  magnet,  viz., 

M  =  NT-  =  -jr-.  (12) 

Furthermore  we  may  calculate  'the  number  of  atoms  which  make  up  an 
elementary  magnet.    Let  N'  be  the  number  of  molecular  magnets  per 


2S9 


W.  W.  ST1FLER. 


[Vol.  XXXIII. 


cubic  centimeter.  Then 
or 


N'M  =  In 


IP  =  ^  (.3) 


If  there  are  «  atoms  per  elementary  magnet  and  each  atom  has  a  mass  of  m 
grams,  then 

nN'm  =  mass  per  unit  volume  =  d. 

But 

m  =  Anin, 

where  A  is  the  atomic  weight  of  the  substance  and  mu  is  the  mass  of  the 
hydrogen  atom.    Hence  we  have 

d  d 

"  ~  N'm  ~  AN'mn  (h) 

Application  of  Theory  to  Experimental  Results. 

Curve  A  of  Fig.  7,  showing  a  as  a  function  of  the  temperature,  indi- 
cates that  the  Curie  point  is  in  the  neighborhood  of  10750  C.  or  13480  Abs. 
From  this  value  a  theoretical  curve  giving  a  as  a  function  of  T  can  be 
calculated  as  follows.  The  curve  OA  in  Fig.  9  gives  us  the  relation 
between  I/Im,  equal  to  <r/o-m,  and  the  parameter  a,  and  Table  VI  gives 
the  values  of  a\am,  calculated  from  equation  (3)  for  various  values  of  a. 
Hence  if  we  can  determine  the  value  of  T  corresponding  to  a  given  value 
of  a,  we  can  at  once  determine  the  corresponding  value  of  a/<rm  either 
from  Table  VI  or  graphically  from  the  curve  of  Fig.  9.  Knowing  <rm 
we  can  then  calculate  the  value  of  a  for  the  given  value  of  T. 

This  relation  between  T  and  a  comes  from  equation  (4)  which  may  be 
written  in  the  form 

l      a  R 


Im     om      MNIm  aT' 


From  equation  (8)  we  have 


Hence 


and 


n  MNIm 
0  =       u  . 


°  1  T 

Om  3/9 


T  = 

a  am 


This  Kivcs  us  the  required  equation,  and  the  values  of  a  'am  are  niven  in 
Table  VI. 


No.  4.] 


MAGNETIZATION  OF  COBALT. 


29O 


Table  VI. 


cosh  a 
sinh  a 

I 

a 

a       cosh  a  1 
(rm     sinh «  a 

U.Ui 

1  no  nnnn 

1UU.UUUU 

1  no  nnnn 

u.uuuu 

ft  1 

1  n  H900 

1  u.uzyy 

1  n  nnnn 

n  H9QO 

0.2 

5.0676 

5.0000 

0.0676 

0.3 

3.4328 

3.3333 

0.0995 

U.-i 

O  fx  1 1  7 

z.oUUU 

ft  1  "21  7 
U.  10  1  / 

U.o 

9  1  A  2G 

Z.UUUU 

u.  iooy 

u.o 

1  QA1  O 

l.ooiy 

1.000/ 

n  1 0  0 
u.iyoz 

0.7 

1.6546 

1.4286 

0.2260 

0.8 

1.5059 

1.2500 

0.2559 

u.y 

1  2QA1 

1  1111 

X.  1 1 1 1 

ft  1Q  ^ft 

1  n 

l.U 

1  2 1  2 1 
1.0 10 1 

1  ftftftft 

1  .uuuu 

ft  21  21 

1  9 

1  1  GGS 

1 .  iyyo 

ft  Q  222 

ft  2AA? 

1.4 

1.1295 

0.7143 

0.4152 

1.6 

1.0849 

0.6250 

0.4599 

1  8 

1  ai 

I.UjOI 

u.  00  00 

ft  ^nn^ 

z.u 

1      7 2 

u.ouuu 

ft  ^27  2 

O.U 

1  ftftAQ 

1  .uu^y 

U.Oooo 

ft  fxl  1  A 

u.o/ 10 

4.0 

1.0007 

0.2500 

0.7507 

5.0 

1.0000 

0.2000 

0.8000 

6.0 

1.0000 

0.1667 

0.8333 

7.0 

1.0000 

0.1429 

0.8571 

8.0 

1.0000 

0.1250 

0.8750 

9.0 

1.0000 

0.1111 

0.8889 

10.0 

1.0000 

0.1000 

0.9000 

12.5 

1.0000 

0.0800 

0.9200 

As  noted  above,  the  work  of  Weiss  and  Onnes  shows  that  the  value  of 
a  at  the  temperature  of  liquid  hydrogen  is  less  than  163.6.  Assuming 
this  value  for  <rm,  the  values  of  a  and  T  corresponding  to  various  values 
of  the  parameter  a  can  be  calculated.    Thus,  for  a  =  0.5 


—  =  0.1639, 

Cm 

from  Table  VI.  Hence 

a  =  0.1639  X  163.6  =  26.8 

and 

3  X  (1,075  +  273) 
T  =   —  X  0.1639  =  13260  Abs.  =  10530  C. 

Carrying  out  similar  calculations  for  other  values  of  a  the  results  given 
in  Table  VII.  are  obtained.  In  this  table,  t  is  the  centigrade  temperature 
corresponding  to  the  absolute  temperature  T. 


29I  W.W.  STIFLER.  [Vol.  XXXIII. 


Table  VII. 


a 

T 

<r 

t 

0.5 

0.1639 

1326° 

26.8 

1053° 

0.7 

0.2260 

1306° 

37.0 

1033° 

1.0 

0.3131 

1266° 

51.2 

993° 

2.0 

0.5373 

1086° 

87.9 

813° 

3.0 

0.6716 

905° 

109.9 

632° 

4.0 

0.7507 

759° 

122.8 

486° 

5.0 

0.8000 

647° 

130.9 

374° 

6.0 

0.8333 

562° 

136.3 

289° 

7.0 

0.8571 

495° 

140.2 

222° 

8.0 

0.8750 

442° 

143.2 

169° 

9.0 

0.8889 

399° 

145.4 

126° 

10.0 

0.9000 

364° 

147.2 

91° 

12.5 

0.9200 

298° 

150.5 

25° 

The  values  of  a  and  /  from  Table  VII.  are  plotted  in  curve  B  of  Fig.  7. 
This  curve  is  of  the  same  general  shape  as  the  experimental  curve,  A, 
but  it  lies  entirely  below  A.  The  difference  between  the  two  curves  is 
about  10  at  o°  C.  and  increases  gradually  to  20  at  6oo°  C.  From  this 
point  on  up  to  10500  C.  the  difference  between  the  two  curves  at  any  tem- 
perature is  practically  constant,  lying  between  20  and  21.  Hence  if 
the  theoretical  curve  is  shifted  up  20  divisions  it  will  coincide  with  the 
experimental  curve  in  the  interval  5000  C.  to  10500  C.  This  is  shown  by 
the  double  circles  in  Fig.  7. 

In  the  interval  above  10700  C.  the  experimental  curve  has  the  general 
form  of  the  hyperbola.    This  agrees  with  the  requirements  of  equation  (9) . 

From  the  data  at  11040  C.  we  can  calculate  the  molecular  field  and 
the  moment  of  the  elementary  magnet.    For  this  temperature  we  have 

T  =  11040  +  2730  =  13770  Abs. 
7m  =  163.6  X  8.77  =  1,435. 


/ 

////, 

1 .400 

11.1 

0.00793 

2,400 

16.6 

0.00692 

3,050 

23.3 

0.00764 

Mean  value  of  ////,  -*  -0.00753. 


Substituting  these  values  in  equation  (10)  we  have 

N.      '       X        'MS     „  -  6,,80. 
0.00753      1,377  -  1.348 


No.  4.)  MAGNETIZATION  OF  COBALT. 

Hence 

Hm  =  NIm  =  6,180  X  1,435  =  8,870,000. 
From  equation  (12)  we  have 


292 


M  = 


3RQ 
NIm 


The  value  of  R  to  be  used  is  that  corresponding  to  one  molecule,  viz., 
R  =  1.36  X  io-"5.  Hence 

3  X  1.36  X  IO-16  X  1,348      ^-      v  in— 20 

M  =  z. — - — —  =  6.21  X  to  20 . 

6,180  X  i,435 

The  number  of  elementary  magnets  per  cubic  centimeter  from  equation 
(13)  is 


N'  = 


Ira  1,435 


M     6.36  X  10 


-  =  2.31  X  10- 


The  number  of  atoms  making  up  an  elementary  magnet  is  given  by 
equation  (14),  viz., 

d  d 
H  ~  N'm  ~  N'AmH' 

The  values  to  be  substituted  are: 

d  =  8.77,         N'  =  2.31  X  io22, 
A  =  59.00,       mH  =  1. 61  X  io-24, 


giving 


59.00  X  2.31  X  io22  X  1.61  X  10- 


u  =  4-oi. 


Hence  four  atoms  of  cobalt  make  up  the  elementary  magnet.  The  value 
4.01  is  far  more  nearly  an  exact  integer  than  the  accuracy  of  the  data 
would  lead  us  to  expect,  and  this  is  strong  evidence  of  the  accuracy  of  the 
value  of  9. 

It  is  interesting  to  compare  these  results  with  those  given  in  Table  V. 
The  results  are  summarized  in  Table  VIII. 

Table  VIII. 


/at  2o0C. 

0 

N 

N/m  =  Hm 

MX  io20 

n 

N> 

Fe 

1,860 

2,120 

756°  C. 

3,850 

6,560,000 

5.15 

2 

4.12  X  1022 

Ni 

500 

570 

376°  C. 

12,700 

6,350,000 

3.65 

6 

1.56  X  1022 

Co 

1,421 

1,435 

1,075°  C. 

6,180 

8,870,000 

6.21 

4 

2.31  X  1022 

As  was  to  be  expected,  the  values  of  /  and  Im  for  cobalt  lie  between  the 
corresponding  values  for  iron  and  nickel.    The  same  is  true  of  N  and  N'. 


293 


W.  W.  STIFLER. 


[Vol.  XXXIII. 


G  how  ever  is  much  higher,  while  the  intrinsic  molecular  field  is  one  third 
larger  than  that  of  iron  or  nickel,  and  the  moment  of  the  elementary 
magnet  is  one  fifth  larger  than  that  of  iron  and  two  thirds  larger  than 
that  of  nickel. 

It  is  very  interesting  to  note  that  the  elementary  magnet  of  cobalt 
consists  of  four  atoms  while  the  elementary  magnet  of  iron,  as  indicated 
by  the  work  of  Kunz,  consists  of  two  atoms  and  that  of  nickel  of  six 
atoms. 

Using  the  laws  of  electrolysis,  another  important  physical  constant 
can  be  calculated,  namely  the  elementary  charge,  e.  This  is  done  as 
follows.    The  number  of  atoms  per  cubic  centimeter  of  cobalt  is 

N*  =  nN'. 

Hence  the  number  of  atoms  per  gram  is 

N  =  N'/d  =  nN'/d 

and  the  number  of  atoms  per  gram  atom  is 

AN  =  nN'Ajd. 

Hence  the  quantity  of  electricity  required  to  deposit  one  gram  atom  is 

nN'A 

Q  =  -d—v-e> 

where  v  is  the  valency.    But  from  the  laws  of  electrolysis 

Q  =  v-  96,540  coulombs 

=  r-9-65  X  io3  c.g.s.  electromagnetic  units. 


Hence 


or 


nN'A  r    ^  3 

— - — ve  =  t"9.65  X  io3 

d 

=  9.65  X  io3  X  d 
C  nN'A 

Substituting  the  values  obtained  above  this  gives 

9.65  x  1  o3  x  s.77 
6     4  X  2.31  X  10**  X  59 
=  1-55  X  I o-20  c.g.s.  electromagnetic  units, 
=  4.65  X  io-10  c.g.s.  electrostatic  units. 


Until  the  recent  work  of  Millikan1  the  accepted  value  for  e  was  4.(>5  X 
1  Piivs.  Rev.,  j*.  pp.  349-397.  19"  • 


No.  4-1 


MAGNETIZATION  OF  COBALT. 


294 


io-10  c.g.s.  electrostatic  units.  This  exact  agreement  is  certainly  far 
better  than  would  reasonably  be  expected,  and  is  further  evidence  of 
the  reliability  of  the  results  at  high  temperatures. 

The  recent  work  of  Weiss  mentioned  above  gives  values  for  x  f°r 
the  interval  from  11560  C.  to  13020  C.  Calculations  of  N,  M,  Hm,  and 
n  based  upon  his  results  are  in  fair  agreement  with  the  results  deduced 
above. 


The  chief  results  of  this  investigation  are  the  following: 

1.  The  saturation  value  of  the  intensity  of  magnetization  of  cobalt 
has  been  determined  at  intervals  of  one  hundred  to  one  hundred  and 
fifty  degrees  throughout  the  interval  from  220  C.  to  11500  C. 

2.  The  "Curie  Point,"  or  point  of  magnetic  transformation  from  the 
ferromagnetic  to  the  paramagnetic  state,  has  been  established  at  10750  C. 

3.  The  curve  giving  cr  as  a  function  of  the  temperature  has  been  shown 
to  be  of  the  same  general  character  as  that  demanded  by  theory,  though 
differing  from  the  theoretical  curve  by  a  constant  amount  throughout 
most  of  its  length 

4.  The  values  of  the  intrinsic  molecular  field,  Hm,  the  moment  of  the 
elementary  magnet,  M,  the  number  of  atoms  in  an  elementary  magnet, 
n,  and  the  elementary  charge,  e,  have  been  calculated  and  found  to  have 
the  following  values: 


The  author  takes  pleasure  in  acknowledging  his  indebtedness  to 

Professor  A.  P.  Carman  for  the  facilities  for  this  investigation,  and  to 

Professor  Jakob  Kunz  both  for  his  general  supervision  of  the  work  and  for 

many  valuable  suggestions. 

Laboratory  of  Physics, 
University  of  Illinois, 
May  8,  1911. 


Summary. 


Hm  =  8,870,000, 
M  =  6.21  X  io-20, 


n 


n  =  4, 
e  =  4.65  X  io-10  E.S. 


VITA 

William  Warren  Stifler  was  born  in  Davenport,  Iowa,  December  22, 
1883.  His  early  education  was  received  in  the  public  schools  of  Detroit, 
Michigan,  Sioux  Falls,  South  Dakota,  and  Upper  Alton,  Illinois,  and  in 
the  Preparatory  Department  of  Shurtleff  College.  He  was  graduated 
from  Shurtleff  College,  Upper  Alton,  Illinois,  in  June  1902  with  first 
honors  in  scholarship,  receiving  the  degree  of  A.B.  During  the  years 
1902-1906  he  was  professor  of  Chemistry  and  Physics  in  Ewing  College, 
Ewing,  Illinois. 

His  graduate  work  was  done  at  the  University  of  Illinois.  In  1906- 
1907  he  was  fellow  in  Physics;  in  1907-1909,  assistant  in  Physics;  in 
1909-1910,  instructor  in  Physics;  in  1910-1911,  fellow  in  Physics.  He 
also  taught  in  the  summer  sessions  of  1907,  1908,  and  1909.  He  received 
the  degree  of  A.M.  in  June  1908.  His  major  work  has  been  in  experi- 
mental physics,  with  mathematics  and  mathematical  physics  as  minors. 

He  is  an  associate  member  of  the  American  Physical  Society  (1907), 
and  is  also  a  member  of  the  Illinois  Chapter  of  Sigma  Xi  (1909)  and  of 
the  Illinois  Chapter  of  the  Gamma  Alpha  Graduate  Scientific  Fraternity 
(1909). 

Publications: 

The  Resistance  of  Certain  Electrolytes  in  a  Magnetic  Field. 

Physical  Review,  28,  pp.  382-385  (1909). 
Tests  on  Certain  Electrical  Insulators  at  High  Temperatures. 

Physical  Review.  32,  pp.  429-432  (1911). 


